We are human beings living inside the zone of radiation. But we can not feel all the radiation with our eyes. Our eyes can detect only those radiation whose wavelengths are within range of 370 nm to 780 nm. This range is called visible range of wavelength. The radiation within this visible range of wavelength is termed as light. Hence, light is an electromagnetic radiation and light has a certain frequency range or wavelength range to be observed by our eyes. Each radiation has its own energy. Light has the energy to stimulate our eyes. The electromagnetic radiation whose wavelength is more than 780 nm is called infrared radiation and it does not stimulate our eyes but stimulates our body as heat. Again the electromagnetic radiation whose wavelength is less than 370 nm is called ultraviolet ray.
There are other radiations whose wavelengths are lesser than that of ultraviolet radiation such as radio wave, X-ray, etc. We also cannot observe these radiations as the wavelength of these radiations are less than 370 nm. Within the visible range of radiation, various wavelengths hold the various colors. The range 597 – 577 nm holds yellow which is in the middle of the visible wavelength range.
Photometry is a process of measuring light by correlating the visual sensation of a standard human observer. The standard viewer or standard human observer has a visual sensation which is the average of that of hundred numbers of visually fit people.
It is already told that the healthy human eyes are sensitive to the visual range of wavelengths of electromagnetic waves. But it is also true that the human eyes are not equally sensitive to all wavelengths of electromagnetic waves within visual range. For some wavelengths, eyes are more sensitive and for some others, they are less sensitive.
Moreover, this sensitivity of eyes for the same wavelength of color can also vary with the intensity of light. That means the visual sensitivity of a color of the particular wavelength may be different in the bright and dim light. Depending on the brightness of the light there are three different types of human vision.
- Photopic Vision – Where high luminance levels adapt the eyes.
- Scotopic Vision – Where low luminance levels adapt the eyes.
- Mesopic Vision – Where intermediate levels of luminance adapt the eyes.
In the photopic vision, the sensitivity of eyes starts increasing from 380 nm and it increases as the wavelength of light increases. At the wavelength of 560 nm, the photopic vision sensitivity reaches its peak and then it starts falling with further increase of wavelength. The wavelength 560 nm corresponds to greenish-yellow color and this is the most eye-catching color in bright light. The photopic vision ends at wavelength 780 nm. The relation between visual sensitivity and wavelength of light is not linear. Hence, the human visual sensitivity to the light can be expressed as a nonlinear function of wavelength V(λ). The function V(λ) is known as relative spectral sensitivity function which is defined as the ratio of the perceived optical stimulus to the incident radiant power as a function of wavelength.
In the scopotic vision (vision in dim light), relation graph between visual sensitivity and wavelength of light is more or less similar to that in photopic vision but the peak of the curve is just shifted to wavelength 507 nm which corresponds to the bluish-green color. That means in the scotopic vision (vision in dim light) the human eyes have the maximum visual sensation to bluish-green color. The relation between visual sensitivity and wavelength in scotopic vision is expressed as another function V’(λ). Hence, the above graph shows two functions. V(λ) is for the Photopic vision (vision in bright light) and V’(λ) for Scotopic Vision (vision in dim light). Both these both functions allow us to derive the photometric quantity. Two graphs have a cross-sectional point at 555 nm. The color corresponding to this wavelength is equally sensitive for Photopic and Scotopic vision.
To relate radiometric quantity to photometric quantity, we have to go for black body radiation. As per practical experiment, the relation between photometric and radiometric has been established. It has been seen that at 2042 K temperature black body gives 60 cd/ sq – cm luminance. As the black body is a perfect diffuser, it has luminous exitance is 60ᴫ lm/ sq – cm at that temperature. If we plot black body spectral power density (radiometric quantity) we will get a graph for 2042 K radiation and we multiply the spectral luminous efficacy (V(λ)) with this curve wavelength by wave length for conversion from radiometric to photometric quantity. The multiplied result gives the new curve of area 0.27598 lumen – Watt/sq – cm.
[NB: Radiometric quantity gives W/sq – cm, but when it is multiplied with spectral luminous efficacy then the unit will be lumen – Watt/sq – cm. that is equivalent to luminous exitance in photometry]
So, now equate 60ᴫ lm/sq – cm to 0.27598 lumen – Watt/sq – cm, we get 60ᴫ/0.27598 = 683 lumen per watt. Thus a constant Km is taken that is equal to 683 lumen per watt in each conversion process.
As we calculated Km in a discrete manner, we can write the conversion equation as,
Where, Xv is any quantity in photometry and Xe,λ any quantity in radiometry.
In continuous form,
This is the process of measuring actual radiation by means of a physical device. Now we can define the spectral density of a radiometric quantity which has symbol X as
Where, subscript e for energetic quantity. X can be flux, energy, irradiance or intensity. The photometric quantity corresponding to a radiometric quantity is obtained from
This equation is written for the Photopic vision only. But for the Scotopic vision above equation can be written as
Km and K’m are proportionality constants. These constants can be defined together with the respective V(λ) functions.